On your 300w PSU what is the amps on the 12v rail? You will have to take the side off your case and look on the PSU and look for the sticker on that has numbers like these.
3.3v = 17a + 5v = 13a + 12v =14a.
If you can give me all the numbers I will be able to tell you if you can use that PSU for sure or not. After looking around at what that card needs for power and it all depends on if you have the 2 chip card.
In a sence it has duel Chips making it a double GPU card. That would require at least 20 amps. So if it is that card you would need a 500w PSU to run it. If It isn't that card you would have to have a 400w or higher PSU.
But sill get me the numbers because you never know. I will link you to some PSU's you can use. The brands you should buy are Corsair, Antec, Seasonic, XFX, Silverstone and some OCZ's brands.
All three PSU's listed are with in your price range. I hope this helps and good luck to you.